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The length of a silver wire of resistance $6 Ω$ , if the length of a similar wire is $80 cm$ and has a resistance of $3 Ω$ is [[1]] $cm$ .

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Detailed Solution

The length of a silver wire of resistance

6 Ω

, if the length of a similar wire is

80 cm

and has resistance of

3 Ω

160 cm

.
Given,
Length of the silver wire

= L_{1}

Resistance of the silver wire

R_{1} = 6 Ω

Length of the wire

L_{2} = 80 cm

Resistance of the wire

R_{2} = 3 Ω

The formula of resistance is given by

R = (\frac{ρL}{A})

Where

ρ =

resistivity of the conductor,

L =

length of the conductor,

A =

area of cross-section of the conductor
Resistance is directly proportional to the length of the conductor.
Therefore,

\Rightarrow \frac{R_{1}}{R_{2}} = \frac{L_{1}}{L_{2}}

Substituting the values,

\Rightarrow \frac{6}{3} = \frac{L_{1}}{80}

\Rightarrow

L_{1} = 80 \times 2

\Rightarrow L_{1} = 160 cm

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